An Essay Concerning Human Understanding, by John Locke

Chapter II

Of the Degrees of our Knowledge

1. Of the degrees, or differences in clearness, of our knowledge: 1. Intuitive. All our
knowledge consisting, as I have said, in the view the mind has of its own ideas, which is the utmost light and greatest
certainty we, with our faculties, and in our way of knowledge, are capable of, it may not be amiss to consider a little
the degrees of its evidence. The different clearness of our knowledge seems to me to lie in the different way of
perception the mind has of the agreement or disagreement of any of its ideas. For if we will reflect on our own ways of
thinking, we will find, that sometimes the mind perceives the agreement or disagreement of two ideas immediately by
themselves, without the intervention of any other: and this I think we may call intuitive knowledge. For in this the
mind is at no pains of proving or examining, but perceives the truth as the eye doth light, only by being directed
towards it. Thus the mind perceives that white is not black, that a circle is not a triangle, that three are more than
two and equal to one and two. Such kinds of truths the mind perceives at the first sight of the ideas together, by bare
intuition; without the intervention of any other idea: and this kind of knowledge is the clearest and most certain that
human frailty is capable of. This part of knowledge is irresistible, and, like bright sunshine, forces itself
immediately to be perceived, as soon as ever the mind turns its view that way; and leaves no room for hesitation,
doubt, or examination, but the mind is presently filled with the clear light of it. It is on this intuition that
depends all the certainty and evidence of all our knowledge; Which certainty every one finds to be so great, that he
cannot imagine, and therefore not require a greater: for a man cannot conceive himself capable of a greater certainty
than to know that any idea in his mind is such as he perceives it to be; and that two ideas, wherein he perceives a
difference, are different and not precisely the same. He that demands a greater certainty than this, demands he knows
not what, and shows only that he has a mind to be a sceptic, without being able to be so. Certainty depends so wholly
on this intuition, that, in the next degree of knowledge which I call demonstrative, this intuition is necessary in all
the connexions of the intermediate ideas, without which we cannot attain knowledge and certainty.

2. II. Demonstrative. The next degree of knowledge is, where the mind perceives the
agreement or disagreement of any ideas, but not immediately. Though wherever the mind perceives the agreement or
disagreement of any of its ideas, there be certain knowledge; yet it does not always happen, that the mind sees that
agreement or disagreement, which there is between them, even where it is discoverable; and in that case remains in
ignorance, and at most gets no further than a probable conjecture. The reason why the mind cannot always perceive
presently the agreement or disagreement of two ideas, is, because those ideas, concerning whose agreement or
disagreement the inquiry is made, cannot by the mind be so put together as to show it. In this case then, when the mind
cannot so bring its ideas together as by their immediate comparison, and as it were juxta-position or application one
to another, to perceive their agreement or disagreement, it is fain, by the intervention of other ideas (one or more,
as it happens) to discover the agreement or disagreement which it searches; and this is that which we call reasoning.
Thus, the mind being willing to know the agreement or disagreement in bigness between the three angles of a triangle
and two right ones, cannot by an immediate view and comparing them do it: because the three angles of a triangle cannot
be brought at once, and be compared with any other one, or two, angles; and so of this the mind has no immediate, no
intuitive knowledge. In this case the mind is fain to find out some other angles, to which the three angles of a
triangle have an equality; and, finding those equal to two right ones. comes to know their equality to two right
ones.

3. Demonstration depends on clearly perceived proofs. Those intervening ideas, which serve
to show the agreement of any two others, are called proofs; and where the agreement and disagreement is by this means
plainly and clearly perceived, it is called demonstration; it being shown to the understanding, and the mind made to
see that it is so. A quickness in the mind to find out these intermediate ideas, (that shall discover the agreement or
disagreement of any other,) and to apply them right, is, I suppose, that which is called sagacity.

4. As certain, but not so easy and ready as intuitive knowledge. This knowledge, by
intervening proofs, though it be certain, yet the evidence of it is not altogether so clear and bright, nor the assent
so ready, as in intuitive knowledge. For, though in demonstration the mind does at last perceive the agreement or
disagreement of the ideas it considers; yet it is not without pains and attention: there must be more than one
transient view to find it. A steady application and pursuit are required to this discovery: and there must be a
progression by steps and degrees, before the mind can in this way arrive at certainty, and come to perceive the
agreement or repugnancy between two ideas that need proofs and the use of reason to show it.

5. The demonstrated conclusion not without doubt, precedent to the demonstration. Another
difference between intuitive and demonstrative knowledge is, that, though in the latter all doubt be removed when, by
the intervention of the intermediate ideas, the agreement or disagreement is perceived, yet before the demonstration
there was a doubt; which in intuitive knowledge cannot happen to the mind that has its faculty of perception left to a
degree capable of distinct ideas; no more than it can be a doubt to the eye (that can distinctly see white and black),
Whether this ink and this paper be all of a colour. If there be sight in the eyes, it will, at first glimpse, without
hesitation, perceive the words printed on this paper different from the colour of the paper: and so if the mind have
the faculty of distinct perception, it will perceive the agreement or disagreement of those ideas that produce
intuitive knowledge. If the eyes have lost the faculty of seeing, or the mind of perceiving, we in vain inquire after
the quickness of sight in one, or clearness of perception in the other.

6. Not so clear as intuitive knowledge. It is true, the perception produced by
demonstration is also very clear; yet it is often with a great abatement of that evident lustre and full assurance that
always accompany that which I call intuitive: like a face reflected by several mirrors one to another, where, as long
as it retains the similitude and agreement with the object, it produces a knowledge; but it is still, in every
successive reflection, with a lessening of that perfect clearness and distinctness which is in the first; till at last,
after many removes, it has a great mixture of dimness, and is not at first sight so knowable, especially to weak eyes.
Thus it is with knowledge made out by a long train of proof.

7. Each step in demonstrated knowledge must have intuitive evidence. Now, in every step
reason makes in demonstrative knowledge, there is an intuitive knowledge of that agreement or disagreement it seeks
with the next intermediate idea which it uses as a proof: for if it were not so, that yet would need a proof; since
without the perception of such agreement or disagreement, there is no knowledge produced: if it be perceived by itself,
it is intuitive knowledge: if it cannot be perceived by itself, there is need of some intervening idea, as a common
measure, to show their agreement or disagreement. By which it is plain that every step in reasoning that produces
knowledge, has intuitive certainty; which when the mind perceives, there is no more required but to remember it, to
make the agreement or disagreement of the ideas concerning which we inquire visible and certain. So that to make
anything a demonstration, it is necessary to perceive the immediate agreement of the intervening ideas, whereby the
agreement or disagreement of the two ideas under examination (whereof the one is always the first, and the other the
last in the account) is found. This intuitive perception of the agreement or disagreement of the intermediate ideas, in
each step and progression of the demonstration, must also be carried exactly in the mind, and a man must be sure that
no part is left out: which, because in long deductions, and the use of many proofs, the memory does not always so
readily and exactly retain; therefore it comes to pass, that this is more imperfect than intuitive knowledge, and men
embrace often falsehood for demonstrations.

8. Hence the mistake, ex praecognitis, et praeconcessis. The necessity of this intuitive
knowledge, in each step of scientifical or demonstrative reasoning, gave occasion, I imagine, to that mistaken axiom,
That all reasoning was ex pracognitis et praeconcessis: which, how far it is a mistake, I shall have occasion to show
more at large, when I come to consider propositions, and particularly those propositions which are called maxims, and
to show that it is by a mistake that they are supposed to be the foundations of all our knowledge and reasonings.

9. Demonstration not limited to ideas of mathematical quantity. It has been generally
taken for granted, that mathematics alone are capable of demonstrative certainty: but to have such an agreement or
disagreement as may intuitively be perceived, being, as I imagine, not the privilege of the ideas of number, extension,
and figure alone, it may possibly be the want of due method and application in us, and not of sufficient evidence in
things, that demonstration has been thought to have so little to do in other parts of knowledge, and been scarce so
much as aimed at by any but mathematicians. For whatever ideas we have wherein the mind can perceive the immediate
agreement or disagreement that is between them, there the mind is capable of intuitive knowledge; and where it can
perceive the agreement or disagreement of any two ideas, by an intuitive perception of the agreement or disagreement
they have with any intermediate ideas, there the mind is capable of demonstration: which is not limited to ideas of
extension, figure, number, and their modes.

10. Why it has been thought to be so limited. The reason why it has been generally sought
for, and supposed to be only in those, I imagine has been, not only the general usefulness of those sciences: but
because, in comparing their equality or excess, the modes of numbers have every the least difference very clear and
perceivable: and though in extension every the least excess is not so perceptible, yet the mind has found out ways to
examine, and discover demonstratively, the just equality of two angles, or extensions, or figures: and both these, i.e.
numbers and figures, can be set down by visible and lasting marks, wherein the ideas under consideration are perfectly
determined; which for the most part they are not, where they are marked only by names and words.

11. Modes of qualities not demonstrable like modes of quantity. But in other simple ideas,
whose modes and differences are made and counted by degrees, and not quantity, we have not so nice and accurate a
distinction of their differences as to perceive, or find ways to measure, their just equality, or the least
differences. For those other simple ideas, being appearances of sensations produced in us, by the size, figure, number,
and motion of minute corpuscles singly insensible; their different degrees also depend upon the variation of some or of
all those causes: which, since it cannot be observed by us, in particles of matter whereof each is too subtile to be
perceived, it is impossible for us to have any exact measures of the different degrees of these simple ideas. For,
supposing the sensation or idea we name whiteness be produced in us by a certain number of globules, which, having a
verticity about their own centres, strike upon the retina of the eye, with a certain degree of rotation, as well as
progressive swiftness; it will hence easily follow, that the more the superficial parts of any body are so ordered as
to reflect the greater number of globules of light, and to give them the proper rotation, which is fit to produce this
sensation of white in us, the more white will that body appear, that from an equal space sends to the retina the
greater number of such corpuscles, with that peculiar sort of motion. I do not say that the nature of light consists in
very small round globules; nor of whiteness in such a texture of parts as gives a certain rotation to these globules
when it reflects them: for I am not now treating physically of light or colours. But this I think I may say, that I
cannot (and I would be glad any one would make intelligible that he did), conceive how bodies without us can any ways
affect our senses, but by the immediate contact of the sensible bodies themselves, as in tasting and feeling, or the
impulse of some sensible particles coming from them, as in seeing, hearing, and smelling; by the different impulse of
which parts, caused by their different size, figure, and motion, the variety of sensations is produced in us.

12. Particles of light and simple ideas of colour. Whether then they be globules or no; or
whether they have a verticity about their own centres that produces the idea of whiteness in us; this is certain, that
the more particles of light are reflected from a body, fitted to give them that peculiar motion which produces the
sensation of whiteness in us; and possibly too, the quicker that peculiar motion is — the whiter does the body appear
from which the greatest number are reflected, as is evident in the same piece of paper put in the sunbeams, in the
shade, and in a dark hole; in each of which it will produce in us the idea of whiteness in far different degrees.

13. The secondary qualities of things not discovered by demonstration. Not knowing,
therefore, what number of particles, nor what motion of them, is fit to produce any precise degree of whiteness, we
cannot demonstrate the certain equality of any two degrees of whiteness; because we have no certain standard to measure
them by, nor means to distinguish every the least real difference, the only help we have being from our senses, which
in this point fail us. But where the difference is so great as to produce in the mind clearly distinct ideas, whose
differences can be perfectly retained, there these ideas or colours, as we see in different kinds, as blue and red, are
as capable of demonstration as ideas of number and extension. What I have here said of whiteness and colours, I think
holds true in all secondary qualities and their modes.

14. Sensitive knowledge of the particular existence of finite beings without us. These
two, viz. intuition and demonstration, are the degrees of our knowledge; whatever comes short of one of these, with
what assurance soever embraced, is but faith or opinion, but not knowledge, at least in all general truths. There is,
indeed, another perception of the mind, employed about the particular existence of finite beings without us, which,
going beyond bare probability, and yet not reaching perfectly to either of the foregoing degrees of certainty, passes
under the name of knowledge. There can be nothing more certain than that the idea we receive from an external object is
in our minds: this is intuitive knowledge. But whether there be anything more than barely that idea in our minds;
whether we can thence certainly infer the existence of anything without us, which corresponds to that idea, is that
whereof some men think there may be a question made; because men may have such ideas in their minds, when no such thing
exists, no such object affects their senses. But yet here I think we are provided with an evidence that puts us past
doubting. For I ask any one, Whether he be not invincibly conscious to himself of a different perception, when he looks
on the sun by day, and thinks on it by night; when he actually tastes wormwood, or smells a rose, or only thinks on
that savour or odour? We as plainly find the difference there is between any idea revived in our minds by our own
memory, and actually coming into our minds by our senses, as we do between any two distinct ideas. If any one say, a
dream may do the same thing, and all these ideas may be produced in us without any external objects; he may please to
dream that I make him this answer:— 1. That it is no great matter, whether I remove his scruple or no: where all is but
dream, reasoning and arguments are of no use, truth and knowledge nothing. 2. That I believe he will allow a very
manifest difference between dreaming of being in the fire, and being actually in it. But yet if he be resolved to
appear so sceptical as to maintain, that what I call being actually in the fire is nothing but a dream; and that we
cannot thereby certainly know, that any such thing as fire actually exists without us: I answer, That we certainly
finding that pleasure or pain follows upon the application of certain objects to us, whose existence we perceive, or
dream that we perceive, by our senses; this certainty is as great as our happiness or misery, beyond which we have no
concernment to know or to be. So that, I think, we may add to the two former sorts of knowledge this also, of the
existence of particular external objects, by that perception and consciousness we have of the actual entrance of ideas
from them, and allow these three degrees of knowledge, viz. intuitive, demonstrative, and sensitive: in each of which
there are different degrees and ways of evidence and certainty.

15. Knowledge not always clear, where the ideas that enter into it are clear. But since
our knowledge is founded on and employed about our ideas only, will it not follow from thence that it is conformable to
our ideas; and that where our ideas are clear and distinct, or obscure and confused, our knowledge will be so too? To
which I answer, No: for our knowledge consisting in the perception of the agreement or disagreement of any two ideas,
its clearness or obscurity consists in the clearness or obscurity of that perception, and not in the clearness or
obscurity of the ideas themselves: v.g. a man that has as clear ideas of the angles of a triangle, and of equality to
two right ones, as any mathematician in the world, may yet have but a very obscure perception of their agreement, and
so have but a very obscure knowledge of it. But ideas which, by reason of their obscurity or otherwise, are confused,
cannot produce any clear or distinct knowledge; because, as far as any ideas are confused, so far the mind cannot
perceive clearly whether they agree or disagree. Or to express the same thing in a way less apt to be misunderstood: he
that hath not determined ideas to the words he uses, cannot make propositions of them of whose truth he can be
certain.